This paper proposes a mechanism for clearance of line congestion and power flow control in a deregulated market environment. The mechanism applies penalties to the bilateral transactions that cause line congestion by increasing the prices of such transactions. The market regulates itself by redefining the transactions and checking again for violations, applying penalties if necessary and repeating the process until all the demand is satisfied without causing line congestion to the system. A bilateral transaction matrix (BTM) creation algorithm developed by the authors and a DC power flow program are integrated as parts of the market mechanism proposed in this paper. The congestion is cleared by the market participants when they reschedule their transactions. This mechanism is useful to study the effects of bilateral transactions on a power system and helps the Independent System Operator (ISO) to create rules and market mechanisms for line congestion clearance and power flow control.